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FINANCIAL MATHEMATICS. MATH 10 – UNIT 4. Students are expected to:. Compare the unit price of two or more given items. Solve problems that involve determining the best buy, and explain the choice in terms of the cost as well as other factors, such as quality and quantity.
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FINANCIAL MATHEMATICS MATH 10 – UNIT 4
Students are expected to: • Compare the unit price of two or more given items. • Solve problems that involve determining the best buy, and explain the choice in terms of the cost as well as other factors, such as quality and quantity. • Compare, using examples, different sales promotion techniques.
Vocabulary • affluent • comfortable • consider • budget • value • efficient • convenient • maturity
Introduction Financial Mathematics is a collection of mathematical techniques that find applications in finance.
Introduction Finance may be defined as the study of how people allocate scarce resources over time. The outcomes of financial decisions (costs and benefits) are spread over time, not generally known with certainty ahead of time, i.e. subject to an element of risk
Decision makers must therefore be able to compare the values of cash-flows at different dates, take a probabilistic view.
Discounting - The time value of money • $1.00 in the hand today is worth more than the expectation of receiving $1.00 at some future date. Thus borrowing isn’t free: the borrower pays a premium to induce the lender to part with his/her money. This premium is the interest.
We assume that: • There is only oneinterest rate. • All investors can borrow and lend at this • (riskless) rate. • The interest rate is constant over time. • The same rate applies for all maturities.
What is Unit Price? • Unit price is the cost of one unit of measure of an item. • Unit price is often used in a grocery store to compare the price of two or more brands of the same item.
How do we determine Unit Prices? • To determine a unit price we will set up a proportion. One side of the proportion will always be: X Dollars 1 Unit (whatever we are buying)
Finding Unit Price Unit Price = Price per Item Measure or Count of Items • Allows shoppers to compare the prices of items quickly and easily.
Metro’s Unit Price Unit Price = $2 50 plates Paper Plates = $0.40 per plate Unit Price = $2 9 oz. For 9 oz. = $0.22 per oz. Cereal For 13.75 oz. Unit Price = $2 13.75 oz = $0.15 per oz. Coffee
Dannon water 32 pack for $4.99 How much per bottle? If each bottle is 16.9 oz., how much per oz? Shop Rite Supermarkets Canada Dry Ginger Ale 6 packs, 3 for $5 How much per can?
Deer Park Water 12 pack for $2.99 Each bottle is 12 oz. How much per bottle? How much per oz? Vanguard Tea Bags Package of 100 2 boxes for $5 How much per tea bag?
Coke 2 liter bottles 4 for $5 How much per liter? How much per bottle? Gatorade 8 pack for $5.99 16 oz to 20 oz bottles How much per bottle? How much per oz (for each size)?
Ruffles Potato Chips 2 bags for $6 16.5 to 20 oz. How much per oz for each size bag? Breyers Ice Cream Buy one get one free $5.79 each 1.75 qt. Containers How much per qt?
Oranges 4 lb. Bag $2.99 Unit Price? M & M’s 14 oz. Bag for $2.69 Unit Price?
Safeway Select Detergent 300 oz. $10.99 What is the Unit Price? Wisk Laundry Detergent 100 oz. $4.99 What is the Unit Price? What is the better buy?
Comparison Shopping: Finding the Better Buy • “Finding the Better Buy” is determining which size, store, or deal will give you the most product for your money. • We use Unit Prices to compare product sizes to find the better buy. • We also use Unit Prices to determine which store or deal will give us the better buy.
Dixie plates $2.49 24 count Unit Price (per plate)? Hefty plates 2 for $4.00 50 count (each pkg.) Unit Price (per plate)? Which is the better buy?
Metro Cheerios 3 for $6 13.75 oz. boxes Unit Price (per oz.)? Vanguard Cheerios 3 for $7.00 15 oz. boxes Unit Price (per oz.)? Which is the better buy?
Metro’s Gatorade 10 for $10 + 2 free 32 oz. bottles Unit Price (per oz.)? Vanguard Gatorade 8 pack for $5.99 20 oz. bottles Unit Price (per oz.)? Which is the better buy?
Metro’s sells 3 different sizes of mayonnaise as follows: Small (10 oz.) for $2.33 Normal size (15 oz.) for $2.67 Big Container (22 oz.) for $3.24 Which one is the better buy?
Metro’s has these paper towels on sale, 8 rolls for $5.99. However they also sell another larger package, 24 rolls for $16.99. You want to buy these since they are on sale, but which is actually the better buy?
Bounty: 8 rolls $5.99 Thirsty: 2 rolls $2.99 Now you want to compare these two brands, which are both on sale. You have determined that you want 8 rolls of paper towels. Which brand will you buy?
Aquafina: 24 pack $3.99 16.9 oz. bottles Deer Park: 12 pack $2.99 12 oz. bottles
Try These! ( Want to volunteer?) 1. Jacob can buy a 32 oz bottle of BBQ sauce for $2.93 or a 36 oz bottle for $3.19. Which is the better buy? 2. John can buy a 8 pencils for $1.25 or a 12 pencils for $2.00. Which is the better buy? 3. Mary made $25.00 for working 7 hours at the mall. How much did Mary make per hour? 4. Lisa paid $158.00 for 3 pair of jeans. What did Lisa pay for each pair of jeans? 5. Bob typed 593 words in 4 minutes. How many words did Bob type per minute?
Try These! Round to nearest hundredth • $2.93 / 32 = $0.09 (better buy) • $3.19 / 36 = $11.6 2. $1.25 / 8 = $0.16 (better buy) $2.00 / 12 = $0.17 3. $25.00 / 7 hours = $3.57 / Hr 4. $158.00 / 3 pair of jeans = $52.67 / jean 5. 593 / 4 minutes = 148.3 words/minute
Homework • #1-8 on pages 8-9
Assignment - # 1 • Check any grocery store. • Find grocery pamphlets. • List 10 grocery items and determine its unit price. • Check your classmate pamphlets, find a similar item and determine which is a better buy.
